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In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…

Numerical Analysis · Mathematics 2025-11-18 G. Makrakis , C. Makridakis , D. Mitsoudis , M. Plexousakis , T. Pryer

We present a numerical method to determine the complex acoustic impedance at the open surface of an arbitrarily shaped cavity, associated to an impinging planar acoustic wave with a given wavenumber vector and frequency. We have achieved…

Fluid Dynamics · Physics 2017-01-31 Danish Patel , Prateek Gupta , Carlo Scalo , Thomas Rothermel , Markus Kuhn

We study a limiting absorption principle for the boundary-value problem describing a hybrid plasma resonance, with a regular coefficient in the principal part of the operator that vanishes on a curve inside the domain and changes its sign…

Analysis of PDEs · Mathematics 2025-10-20 Maryna Kachanovska , Étienne Peillon

We investigate the sound absorption in quark matter due to the interaction of the sound wave with the precritical fluctuations of the diquark-pair field above $T_c$. The soft collective mode of the pair field is derived using the time…

High Energy Physics - Phenomenology · Physics 2016-10-14 B. O. Kerbikov , M. S. Lukashov

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…

Optimization and Control · Mathematics 2021-03-30 Konstantin Pieper , Bao Quoc Tang , Philip Trautmann , Daniel Walter

We report on experiments of perfect absorption for surface gravity waves impinging a wall structured by a subwavelength resonator. By tuning the geometry of the resonator, a balance is achieved between the radiation damping and the…

Fluid Dynamics · Physics 2019-01-30 Eduardo Monsalve , Agnes Maurel , Philippe Petitjeans , Vincent Pagneux

The optical theorem is a powerful tool of scattering theory that directly relates the extinction cross section of a scatterer to its forward scattering amplitude. While widely used in electromagnetism and optics, its application in…

The coherent stochastic resonance is observed and studied with multi-step periodic signal in continuous medium having two absorbing boundaries. The general features of this process are exihibited. The universal features at the resonance…

Condensed Matter · Physics 2009-10-31 Asish K. Dhara , Tapan Mukhopadhyay

In this work we have developed a technique for the measurement of the resonance curve of Helmholtz resonators as a function of filling with beads and sands of different sizes, and water as the reference. Our measurements allowed us to…

Classical Physics · Physics 2023-07-06 M. V. Indenbom , S. P. Pogossian

Consider the wave propagation in a two-layered medium consisting of a homogeneous compressible air or fluid on top of a homogeneous isotropic elastic solid. The interface between the two layers is assumed to be an unbounded rough surface.…

Analysis of PDEs · Mathematics 2016-08-22 Yixian Gao , Peijun Li , Bo Zhang

Traditional microperforated panels (MPPs) and metamaterial-based sound absorbers rely on local resonances or multi-resonator designs, which limit their bandwidth, angular applicability, and ease of fabrication. Leveraging the reciprocity…

Applied Physics · Physics 2025-01-22 Jinjie Shi , Jie Luo , Chenkai Liu , Hongchen Chu , Yongxin Jing , Changqing Xu , Xiaozhou Liu , Jensen Li , Yun Lai

The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough…

High Energy Physics - Phenomenology · Physics 2024-08-02 Tomona Kinugawa , Tetsuo Hyodo

We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a nontrapping obstacle, with boundary data coming from plane-wave incidence, by the solution of the corresponding boundary value problem where the…

Numerical Analysis · Mathematics 2023-06-23 Jeffrey Galkowski , David Lafontaine , Euan A. Spence

We study the one-dimensional Helmholtz equation with (possibly perturbed) quasiperiodic coefficients. Quasiperiodic functions are the restriction of higher dimensional periodic functions along a certain (irrational) direction. In classical…

Analysis of PDEs · Mathematics 2026-02-10 Pierre Amenoagbadji , Sonia Fliss , Patrick Joly

Causality constraints are known to bind sound absorption to a limit that can only be achieved by optimizing the system bandwidth for a specific material thickness. This limit is defined on the assumption of a one-port system, generally…

Asymmetric sound absorption is essential for advanced acoustic manipulation. However, current frequency modulation and broadbanding highly depend on geometric reconfiguration, leading to inevitable structural complexity that impedes their…

Applied Physics · Physics 2026-04-06 Keqiang Lyu , Mohamed Farhat , Ying Wu

Wave absorption metamaterials have been an enduring topic over the past two decades, propelled not only by novel scientific advances, but also by their extensive application potential. In this review, we aim to provide some general insights…

Applied Physics · Physics 2022-05-24 Sichao Qu , Ping Sheng

Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…

Numerical Analysis · Mathematics 2020-05-29 Lehel Banjai , Christian Lubich , Joerg Nick

We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved…

Numerical Analysis · Mathematics 2023-05-03 Samuel F. Potter , Maria K. Cameron , Ramani Duraiswami

Almost all known image reconstruction algorithms for photoacoustic and thermoacoustic tomography assume that the acoustic waves leave the region of interest after a finite time. This assumption is reasonable if the reflections from the…

Analysis of PDEs · Mathematics 2015-06-16 L. Kunyansky , B. Holman , B. T. Cox